Method of straightening a reformat for navigation and quantification

ABSTRACT

A method of producing an improved straightened reformat is presented in which cross sections are calculated perpendicular to an elongate subject described within an object data set, a reference direction-is-determined in each cross sectional slice and a new object data set is created by concatenating the cross sectional slices, each cross sectional slice orientated so that the reference directions in the cross sectional slices are aligned. Various methods are presented by which the reference direction is determined within each cross sectional slice, including propagation from an original reference direction and optimization using determined reference directions as boundary conditions.

The invention relates to a method for producing an object data setdescribing a straightened reformat from an original object data setcontaining an elongate subject, from which an initial cross sectionalslice is created transverse to the elongate subject and at least onefurther cross sectional slice is created transverse to the elongatesubject.

The clear visualization of complex and tortuous structures within athree dimensional object data set is a difficult problem within imaging.Medical imaging in particular contains many examples of tortuousobjects. Arteries, veins, nerves and the lower digestive tract are allexamples of structures which present with a large degree of tortuosityin relation to the surrounding tissue. This inherent anfractuositypresents difficulty when these structures are displayed following theuse of traditional imaging methods.

Modern imaging allow the viewing of 3 dimensional object data on a 2dimensional computer screen or some other display device. For practicalpurposes, a display device includes a hard copy of an image such as anX-ray film or a print out. The data is usually the output of an imagingprocedure, e.g. computed tomography, magnetic resonance imaging,ultrasound, and contains information for the quantification andqualification of the object under examination. The inherent limitationsof a 2 dimensional screen constrict the display of information to flatimages, but a variety of techniques are commonly employed to maximizethe utility of these images. While volume data has been traditionallyshown as a series of 2 dimensional slices, the technique of volumerendering, for example, allows a 3 dimensional object to be displayed asa projection onto the 2 dimensional screen while including featureswhich are redolent of a solid object. These features, such as shading toindicate a solid surface, or partial shading to indicate a block ofsolid structure, give the impression of a spatially extended object andtrick the eye of the viewer into interpreting the flat projection as a 3dimensional shape.

Volume rendering, as applied to tortuous objects set within a widervolume of tissue, can highlight the position of the twisting objectwithin the tissue. Commonly, the tortuous object under inspection can berendered as solid within a surrounding tissue volume which must bynecessity be rendered at least partially transparent to allow thevisualization of the immanent flexuous structure. The extent of thewinding and twisting structure can then be seen. However, the entirevolume of tissue, including any anatomical ambages is usually onlyviewed from one direction, the direction which is presented on thescreen. Any irregularities, variations in diameter and rapid curving ofthe structure along its axis are likewise viewed from the same directionand an unrepresentative distortion of the visual information can ensue,depending on the direction of projection. In particular, narrowings orwidenings of a tubular tortuous structure, which may be indicative of anunderlying disease process, may be rendered unclear.

In part the problem of how to analyze narrowings and widenings withinsome tubular structure can be solved by always reconstructing the objectalong one of its natural axes. For example, a narrowing along a large,straight artery will be clearly visible in a 2 dimensional slice whichincludes the length of the artery. Unfortunately, this is not a viableoption when the artery, or other structure, is ambagious. The inherenttortuosity of such a structure makes it extremely difficult to presentthe 3 dimensional image information into planes which clearly expose asufficient length of the structure to accurately recognize the existenceof narrowing or widening. Because of the twisting nature of the tortuousstructure, it twists in and out of any 2 dimensional plane that isreconstructed. Trying to track the entire length of the structurebecomes time consuming and laborious as more and more 2 dimensionalplanes are reconstructed at an ever greater range of positions andangles within the original object data set.

In part the problem of viewing twisting, tortuous structures has beensolved by a method of reconstruction known as straightened reformatting,in which a three dimensional object data set containing image datarepresenting a tortuous structure can be reformatted to produce afurther image in which the twisting structure is displayed in astraightened conformation. The tortuous structure is presented on thescreen as though it has been gripped at both ends and pulled straight.Any inherent tortuosity is therefore removed. A method of achieving thisis presented in WO 01/37219 A1. This discloses a method in whichvolumetric images are reformatted into rectilinear data by isolating thetortuous structure within the volumetric data, determining the axis ofthe structure and constructing planes at selected points along thisaxis. The volumetric data is then reformatted along these planes and thefinal image reconstituted from the sequence of plane images.

However, when a new data set is made by simply reconstructing crosssectional slices at intervals and then assembling the slices to create anew block of data there will be small discontinuities in the resultingimage derived from the new data set.

It is an object of the invention to produce a straightened reformatwhich reduces discontinuities in the array of data in the new objectdata set. This is achieved according to the method of our inventionwhich is characterized in that, a reference direction is determined ineach cross sectional slice, the object data set is created byconcatenating the cross sectional slices, each cross sectional sliceorientated so that the reference directions in the cross sectionalslices are aligned.

Cross sectional slices of data can be calculated and produced in anobject data set at any angle within the volume represented by the dataset. The general method of straightened reformatting rests on anassumption that cross sectional slices made at orientations which areperpendicular to the tortuous structure and then stacked one on top ofeach other will, if they include the tortuous structure at the sameposition within each slice, produce a new object data set in which thedata points describing the tortuous structure are collected together insuch a way that the display of the new data set produces an image of thematerial in the tortuous structure in a locally defined volume. Thislocally defined volume is a straight line, or tube.

The cross sectional slices used to sample the data points describing thetortuous structure within the block of tissue can be constructed inseveral ways. One such way is disclosed in document WO 01/37219 A1, butalternative methods exist. Most other methods are based on the initialidentification of the axis of the structure and there are several knowntechniques for identifying this axis. As an example, one method which isapplicable to a tubular structure involves segmenting the length of thetube from the surrounding tissue and then incrementally ‘thinning’ thediameter of the tube until only the axis remains.

The result of any of these cross sectional sampling methods is a seriesof such slices, each including a cross section of the tortuous structurewhich is essentially perpendicular to the slice throughout the lengthalong which it intersects that slice. As long as each cross sectionalslice remains centered on the tortuous structure as it is calculated inthe object data set, the included section of tortuous structure remainsin the center of each cross sectional slice. When they are finallystacked, these cross sectional slices produce a new object data setwhich contains some of the original information describing the originaltissue volume, but orientated in a new way. The successive portions ofthe tortuous structure, each contributed from a different crosssectional slice, reformulate the tortuous structure into a straightstructure.

A reference direction can be determined in each cross section. Thisreference direction is a mathematical construct which defines anorientation within each calculated cross section. As such, the referencedirection can be imagined as running from the cross sectional portion ofthe original anfractuous structure contained in the center of thecalculated cross section, outwards towards the edge of that crosssection of data. In doing so, it can be imagined as forming a directionin which the cross section can point, or be orientated. Such a referencedirection as described allows the assembly of cross sections to beorientated within the new object data set in a reproducible andunambiguous way.

If the consecution of cross sections is formed into a stack, with thecenters of the cross sections containing the portions of the tortuousstructure lined up in one axial direction, then the reference directionswill all extend radially outwards from this axial center. Thesereference directions now provide a mode in which the various crosssections in the stack, or catena, can become aligned, or orientated,with respect to each other.

According to the invention, just such a catena of cross sections isformed and the array of cross sections individually rotated until allthe reference directions are pointing along the same angular directionabout the central radial axis. This aligns the various cross sectionsinto a specific conformation. The reference directions, once determinedin each cross sectional slice, remain fixed in direction.

The reference directions could be determined in some random pattern, butthis would result in a random correlation of slice orientations.Alternatively, known mathematical descriptions could be used to producea set of reference directions, for example, the Frenet frame, whichprovides a mathematical description of a 3 dimensional curve in terms of3 orthogonal vectors may be used to provide each cross section with areference vector related to the curvature and tortuosity of the centralaxis. The set of these vectors, one for each slice, would thenconstitute the necessary reference directions. Alignment of the crosssections would then proceed according to the rest of the invention.However, mathematical methods have their own inherent limitations, forexample the classic Frenet reference system produces a set of vectorswhich can accurately describe a twisting curve but which may containdiscontinuities between themselves as a result of that very tortuositythey seek to describe. Details of these vectors and their calculationcan be found in advanced mathematical texts and also in Ph.D. thesis‘Blood vessel segmentation, quantification and visualization for 3D MRand spiral CT angiography’ by Bert Verdonck, presented on 28 Oct., 1996,Ecole Nationale Supérieure des Télécommunications.

Instead, according to one aspect of the invention, an initial referencedirection is determined in the initial cross section and then used asthe basis for determining the successive reference directions in thefollowing cross sections.

This subsequent derivation of further reference directions can beachieved in several ways. In one implementation of the invention, thisinitial reference direction is propagated into each of the subsequentcross sections. As such, the original orientation of the first referencedirection is transferred mathematically onto each of the further crosssections, taking into account the relative orientation of the two crosssections with respect to each other. This is repeated for each pairingof a further cross section with the initial cross section. Thispropagation can mathematically occur in a variety of ways, the mainpoint being to achieve a set of new reference directions, each one in adifferent cross sectional slice, by which the slices can be aligned.

A simple mathematical example can serve as an illustration of how thisis achieved in practice. The curve which constitutes the axis of thetortuous structure is described at all points by a tangent vector whichidentifies the direction in which the curve moves. The positions atwhich cross sections cross this curve describe a series of points alongthis curve and for any of these points a reference direction can befound which is perpendicular to the tangent at that point. Thisreference direction can be transferred mathematically to the next pointalong the curve and repositioned there. At this next point thetranslated reference direction simply describes an orientation in spaceand will not reside in the cross section which coincides with the nextpoint along the curve if the line describing the curve has deviated inany way from the previous tangential direction. However, the translatedreference direction can be propagated into this adjoining cross sectionif a method can be found of changing the direction in which it pointswithout losing the connection between the original and resultantdirections.

This can be achieved if a third direction is defined perpendicular tothe tangent vector at the new point. Any line which is itselfperpendicular to the second tangent can take any one of 2π orientationsabout the tangent because the line can sweep out a plane while remainingperpendicular to the tangent. If an orientation is now defined bydefining another plane, one which contains the tangent, we can forge adirection for the third line by stipulating that it be perpendicular tothis plane. Such a plane is formed by the direction of the tangent andthe previous point on the curve of the axis. Alternatively, an equallyviable, but different plane, would be formed by the new point on thecurve and the previous tangent direction. In both cases a new plane isdefined which cuts through the point on the curve to which the originalreference direction has been translated. It is now possible to constructa straight line which traverses this plane at the new point. The newreference direction in the new cross section is now produced bymathematically rotating the translated reference direction around thisnew line until it resides fully within the cross section. Thisorientation within the cross section constitutes the new referencedirection.

This process may be repeated for all subsequent cross sectionsthroughout the entire array of cross sections.

There are other known mathematical ways in which a reference directionin any one plane may be propagated in any other plane. For example,further examples are given in ‘Blood vessel segmentation, quantificationand visualization for 3D MR and spiral CT angiography’.

In an alternative implementation, the reference direction in the initialcross sectional slice is propagated into the following slice to create anew reference direction, and this new direction is then propagated intothe slice following that to make the subsequent reference direction.This process is repeated throughout the continuation of slices until allslices have an associated reference direction. In this variation of themethod there is a closer relationship between each reference directionand the reference direction in the following slice. The process ofstacking the slices and aligning them according to the referencedirections can then proceed as normal.

A different embodiment for setting the reference direction in each crosssectional slice is also possible. In this further aspect of theinvention both an first and a final cross section can be chosen from thefull group of cross sections and a reference direction determined ineach. These two determined reference directions are then taken to act asconstraints on the set of intermediate reference directions. Theintermediate reference directions can then be derived using the firstand final reference directions as end points, and in such a way that thechange of orientation of the reference directions is optimized along thecurve between the first and final reference directions. This avoidsdiscontinuities from one cross sectional slice to another in thereconstructed straightened reformat.

This can be achieved in practice as follows. The technique is applicableto a reconstruction of a straightened reformat over a continuous lengthof tortuous structure in which a first and a final cross section can bedetermined. These may not necessarily be the original initial and finalcross sections of the entire new object data set describing thestraightened reformat. The constraining reference directions are chosenor determined in the first and final cross sectional slices and anintegral minimization is performed over the intervening referencedirections by integrating the changes in reference direction orientationover the entire collection of reference directions and minimizing theresultant integral value. Numerical solutions are known in the art bywhich this can be achieved. The result is an overall set of referencedirections which change minimally in orientation across the length ofthe reconstructed structure.

This process of optimization may then be taken further. If first andfinal reference directions are set within the first and final crosssections, an additional reference direction, within some additionalcross section between the first and final cross sections, may also bedetermined independently and all three reference directions used asboundary points. The cross sectional slices between the first and finalcross sections then fall naturally into two groups, those between thefirst and the additional cross sections and those between the additionaland the final cross sections. The respective reference directions ateither end of these two subsets of cross sections act as boundaryreference directions allowing the optimization of the interveningreference directions within each set.

The choice of the original reference direction in the propagationembodiments, or the choice of any of the determined reference directionsin the optimization embodiments of the invention, is relatively easy.They may simply by chosen by the user. This would occur for example whenthe particular anatomy of the structure under consideration renderedspecific orientations more useful than others. For example, if thestructure were a branching artery, reference directions might be chosento produce orientations in the final images in which the branchingstructure of the artery was rendered particularly clearly. If there wereno particular visual constraints on the orientations of any of thereference directions then they could be chosen automatically from withinthe image manipulation system. As an example of how this might be done,it has already been mentioned that it is possible to define a series ofmathematical vectors which describe the twisting curve. Armed with sucha set of vectors, a reference direction can be chosen to be themathematical vector which is closest to the nearest axis of aco-ordinate system describing the original object data set. In otherwords, the problem of finding a first reference direction can be solvedmathematically, and methods exist by which this can be done.

These and other aspects of the invention will be further elucidated anddescribed with respect to the drawings.

FIG. 1 shows a use of the invention in practice.

FIG. 2 shows the formation of a new object data set according to theinvention.

FIG. 3 shows the new object data set according to the invention.

FIG. 4 shows a reference direction oriented within a cross sectionalslice, according to the invention.

FIG. 5 shows the cross sections in the new object data set withreference directions according to the invention superimposed.

FIG. 6 shows the cross sectional slices reoriented according to theinvention so as to bring all the references into line.

FIG. 7 shows a method for performing the propagation of the referencedirection from one cross sectional slice into another, according to theinvention.

FIG. 8 shows an optimization of the change of reference directionaccording to the invention.

FIG. 9 shows an optimization of the change of reference direction overtwo subsets of intervening slices, according to the invention.

FIG. 1 shows a use of the invention within imaging practice. 101 is anobject data set containing some tortuous structure 102. In this case 102might be an artery. Multiple cross sections 103 can be calculated, eachcontaining a small cross section of the tortuous structure 102. Thetortuous structure is thus sampled from without the original object dataset 101.

FIG. 2 shows the formation of the new object data set according to theinvention. The tortuous structure, 201, in this case an artery, isreconstructed by reconstructing a new object data set from theconcatenation of cross sections 203. The cross sections formed from theoriginal object data set are depicted in these drawings as square.However, this is not a prerequisite of the method. In fact, any shape ofcross section may be formed of any size as long as it contains crosssectional information about the tortuous structure in such a way that itcan be concatenated with at least one other such cross section.

FIG. 3 shows the new object data set reconstructed according to theinvention. The original tortuous structure 301 is now reconstructedthrough the reconstruction of the cross sections 302. This new objectdata set can now be viewed in the same way as any other object data set.Slices through any part of the new object data set may be formed, it maybe subjected to volume visualization techniques and subjected tofly-throughs along the center of the tortuous structure 403.

FIG. 4 shows a reference direction 402 oriented within a cross sectionalslice 401, according to the invention. The reference direction 402 canmathematically point out any direction about the center of the crosssectional slice 401 containing the portion of the tortuous structure.

FIG. 5 shows the cross sections in the new object data set withreference directions according to the invention superimposed. The set ofcross sectional slices 501 each contain a portion of the tortuousstructure 502 and each contains a reference direction 503.

FIG. 6 shows the cross sectional slices 601 reoriented about the centralportions 602 containing the cross sections of the tortuous structureaccording to the invention so as to bring all the reference directions603 into line.

FIG. 7 shows a method for performing the propagation of the referencedirection from one cross sectional slice into another, according to theinvention. The Figure shows the method as applied to 2 dimensions. Themethod can be easily extended to 3 dimensions. A 2 dimensional curve 701is shown with 2 perpendicular cross sectional slices 702 and 703crossing the curve at points 704 and 705. A tangent vector can bedefined at both these points, vector 706 being the tangent at point 704on slice 702 and vector 707 being the equivalent at point 705 on slice703. A representative reference direction 708, a vector, is definedwithin cross sectional slice 702, originating at point 704 and this istransferred to originate from point 705 in slice 703. Because of thecurvature of 701, the vector 708 no longer lies within the slice at 705,viz. 703. A new axis is therefore defined at point 705, being the lineperpendicular to the plane containing 707 and point 704. Because theline 701 is constrained to lie within 2 dimensions, the plane containingboth 707 and 704 is itself in the same plane as the Figure. This wouldnot necessarily be so if the method were extended to more than 2dimensions. The new axis is shown as 710 and vector 708 originating atpoint 705 is rotated around 710 until it lies within the slice 703. Inso doing, it becoming the new reference direction 709.

FIG. 8 shows an optimization of the change of reference directionaccording to the invention. A catena of cross sectional slices 801 isshown, with the first slice 802 and the final slice 803 containing afirst reference direction 804 and a final reference direction 805. Theseare both used as boundary reference directions. The interveningreference directions 806 are then found by using an optimizationstrategy which takes 804 and 805 as boundary reference directions.

FIG. 9 shows an optimization of the change of reference direction overtwo subsets of intervening slices, according to the invention. Here, asimilar set of cross sectional slices, 901 are shown with first andfinal slices 902 and 903 having determined reference directions 904 and905. Now, however, an additional cross sectional slice 906 in theintervening group of cross sectional slices also has a determinedreference direction 907. All the intervening reference directionsbetween 904 and 907 and between 907 and 905 are now found from anoptimization strategy which uses the determined reference directions inslices 902, 903 and 906 as boundary conditions.

The result of the invention as described is a new object data set whichcan be displayed in image form on a screen and examined for usefulinformation about the original sinuous structure. The method ofreconstruction retains important original information about the tortuousshape. In particular, the width or diameter of the structure can be moreeasily viewed when presented as a straightened reformat. If the flexuousstructure rendered straight is also tubular and therefore has aninternal surface, then the bore, or internal diameter, of the structurecan also be more easily viewed using this invention.

The invention thus offers a powerful viewing tool for the visualizationof twisting structures within volumes of tissue and the resultantreformulated image data can be manipulated using standard image andvolume manipulation techniques. For example, 2 dimensional image slicescalculated across the new object data set can be constructed to includelongitudinal cross sections of the straightened structure. They can becalculated at a succession of different angles in relation to theinformation within the new object data set and so can present differentviews of the straightened structure. A succession of these slicespresented continuously would give the impression of the straightenedstructure rotating and allow the straightened structure to be viewedfrom a succession of different angular orientations. Attributes such asthe thickness of the wall of the structure can now be clearly seen inrelation to the rest of the structure. The inherent inventive methodallows this to be achieved quite easily. Cross sectional slices, eachone containing the axis of the new straightened structure, can becalculated from within the new object data set at a succession of anglesrelative to the position of the aligned reference directions.

It is from the embodiments through which the reference directions acrossall cross sections derive their orientations that the invention derivesit's power. This invention allows the reconstituted planes which arederived from the original data set to retain some spatial relationshipwith respect to each other. In this way distortion within the resultingimage data is minimized. A tortuous structure which is itself twistingin space twists also in relation to itself As each subsequent crosssectional plane along the twisting axis is reconstructed and stacked ontop of the previous one it can potentially be orientated at any anglewithin the 2π radians around the axis of the new structure which isformed. But only some orientations of cross sections allow the resultingstraightened reformat to preserve the original interesting featuresinherent in the tortuous object. By mathematically relating thereference direction in each cross sectional slice to some otherreference direction in the body of cross sections, the information inthe new object data set retains physical consistency.

As an example, if the original tortuous structure were an arterycontaining some structural mass on some part of the internal wall, itwould be expected that for a straightened reformat to be meaningful,successive cross sections including the mass must be oriented relativeto each other in such a way as to maintain the topological relationshipswithin the mass and between the mass and the artery wall. Without havingdetailed knowledge of the structure of the tortuous object it isreasonable to assume that there exists some specific orientation ofcross sections which, when adopted, will maximize the retention oforiginal topographical information, but without a complete knowledge ofthe arrangement and structure of the tortuous object, it is frequentlyimpossible to tell what these exact orientations should be. Without thisa priori information, any plane which is reconstructed and stacked ontop of the previous one in a straightened reformat image may conceivablybe placed at any angle within 2π about the axis of the tortuousstructure which forms the basis of the reconstruction. In the case ofthe artery with the adherent internal mass, this has the potential toproduce discontinuities in the representation of the physical structurewith portions of the mass becoming shifted around from each other in thefinal reconstruction and vital visual information consequently becomingobscured. If such an image were used for diagnostic purposes an errormight occur. If, however, a mathematical relationship exists between theorientations of the cross sections, and this invention achieves thisthrough use of the reference directions and their relationship to eachother, the cross sectional slices in the new object data set areconstrained to an alignment which retains the relationship of theoriginal information being represented. In the case of the artery,successive slices retain a relative orientation to each other and thereconstruction retains topological relationships within the mass andbetween the mass and the artery wall.

The ability to optimize intervening reference directions in relation tofixed, chosen reference directions allows the invention to handle imagescontaining branching structures. Using the invention, a branching arterycan be straightened out and the relative orientations of the branchesbrought into line by the viewer. If the viewer fixes the direction ofthe reference directions at two end points and any intervening point, toinclude say, any branching points, the invention then straightens outand untwists the image of the intervening tissue in relation to thechosen points. The resulting object data set will contain the relativeorientations of the branching points in one plane. This may be appliedto any number of branching points in succession as an optimizationprocess can be applied to any number of subsets of intervening crosssections, as long as the two reference directions at either end of thesuccession of cross sections have been determined. Indeed, any or bothof the end point reference directions can also be a reference directionfor a branching point.

The utility of the invention allows further application to differentimaging problems. For example, reconstruction of successive crosssectional slices using related reference directions allows thereconstruction of a tubular structure for the purposes of internalvisualization. An example of this is the reconstruction and manipulationof volume data describing colon tissue. Techniques for this are sosophisticated that a fly-through can now be performed, that is, asuccession of images presented to the viewer which give the viewer theimpression of travelling internally through the length of colon. This isa useful tool in diagnosis. The method of the invention may be appliedto the colon reconstruction methods to produce a fly-through withreduced changes in angular orientation as the visualized colon istraversed, that is, a fly-through can be produced which produces less ofa sensation of sea sickness in the viewer.

1. A method of producing an object data set describing a straightenedreformat from an original object data set containing an elongatesubject, from which an initial cross sectional slice is createdtransverse to the elongate subject and at least one further crosssectional slice is created transverse to the elongate subject,characterized in that, a reference direction is determined in each crosssectional slice, the object data set is created by concatenating thecross sectional slices, each cross sectional slice orientated so thatthe reference directions in the cross sectional slices are aligned.
 2. Amethod as in claim 1, characterized in that the determination of thereference direction in each cross sectional slice comprises the methodof determining an initial reference direction in the initial crosssectional slice, deriving the reference directions in the at least onefurther cross sectional slices from the initial reference direction bypropagation.
 3. A method as in claim 2, characterized in that thedetermined initial reference direction is propagated directly into eachof the at least one further slices.
 4. A method as in claim 2,characterized in that the initial and the at least one further crosssectional slices form a consecution of successive cross sectional slicesand the reference direction in each cross sectional slice in the atleast one further cross sectional slices is derived from the referencedirection in the preceding slice by propagation.
 5. A method as in claim1, characterized in that the determination of the reference direction ineach cross sectional slice comprises the method of determining a firstreference direction in a first cross sectional slice, independentlydetermining a final reference direction in a final cross sectionalslice, so that there is at least one intervening cross sectional slicebetween the first and the final cross sectional slices, deriving thereference directions in the intervening cross sectional slices byoptimizing the change of reference direction throughout the interveningcross sectional slices while using the first and final referencedirections in the first and final cross sectional slices as boundaryconditions.
 6. An optimization of the change of reference direction asin claim 5, characterized in that, the change in relative orientationbetween any two consecutive reference directions from the firstreference direction in the first cross sectional slice to the finalreference direction in the final cross sectional slice is minimized. 7.A method as in claim 5, characterized in that, An additional crosssectional slice is chosen from the group of at least one interveningcross sectional slices between the first and the final cross sectionalslices, an additional reference direction is determined in theadditional cross sectional slice, the reference directions in theintervening cross sectional slices between the first and the additionalcross sectional slice and between the additional and the final crosssectional slices are derived by optimizing the change of referencedirection throughout the cross sectional slices while using the first,additional and final reference directions as boundary conditions.
 8. Amethod as in claim 1, characterized in that the cross sectional slicesare aligned within the object data set describing the straightenedreformat in such a way that their reference directions are at the sameangular orientation within the object data set.
 9. The display of anobject data set created according to claim
 1. 10. A computer program,containing instructions for the production of a straightened reformatfrom successive cross sectional slices from within an object data set,characterized in that, the computer program further containsinstructions for a reference direction to be determined within eachcross sectional slice, and further instructions for the cross sectionalslices to be aligned by alignment of the individual referencedirections.
 11. A workstation, configured for the purposes of producing,displaying and using images and containing instructions for theproduction of a straightened reformat from successive cross sectionalslices from within an object data set, characterized in that theworkstation further includes instructions for a reference direction tobe determined within each cross sectional slice, and furtherinstructions for the cross sectional slices to be aligned by alignmentof the individual reference directions.